Scopus İndeksli Yayınlar Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8651
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Article Citation - WoS: 73Citation - Scopus: 98Anomalous Diffusion Models With General Fractional Derivatives Within the Kernels of the Extended Mittag-Leffler Type Functions(Editura Acad Romane, 2017) Yang, Xiao-Jun; Baleanu, Dumitru; Tenreiro Machado, J. A.; Baleanu, Dumitru; Machado, J. A. Tenreiro; MatematikThis paper addresses the new general fractional derivatives (GFDs) involving the kernels of the extended Mittag-Leffler type functions (MLFs). With the aid of the GFDs in the MLF kernels, the mathematical models for the anomalous diffusion of fractional order are analyzed and discussed. The proposed formulations are also used to describe complex phenomena that occur in heat transfer.Article Citation - WoS: 19Citation - Scopus: 20Fractional Calculus Analysis of the Cosmic Microwave Background(Editura Acad Romane, 2013) Tenreiro Machado, J. A.; Baleanu, Dumitru; Stefanescu, Petruta; Tintareanu, Ovidiu; Baleanu, Dumitru; MatematikCosmic microwave background (CMB) radiation is the imprint from an early stage of the Universe and investigation of its properties is crucial for understanding the fundamental laws governing the structure and evolution of the Universe. Measurements of the CMB anisotropies are decisive to cosmology, since any cosmological model must explain it. The brightness, strongest at the microwave frequencies, is almost uniform in all directions, but tiny variations reveal a spatial pattern of small anisotropies. Active research is being developed seeking better interpretations of the phenomenon. This paper analyses the recent data in the perspective of fractional calculus. By taking advantage of the inherent memory of fractional operators some hidden properties are captured and described.Book Part Numerical Solutions for Odes With Local Fractional Derivative(de Gruyter Open Ltd, 2015) Baleanu, Dumitru; Tenreiro Machado, J. A.; Yang, Xiao-Jun; Machado, J. A. TenreiroIn this chapter an efficient numerical algorithm for solving ODEs using the extended differential transform method via the generalized local fractional Taylor theorem is presented. Four examples are studied in order to illustrate the proposed technique.Article Citation - WoS: 1Citation - Scopus: 1Analysis of the Nano-Surface of a Modified Glassy Carbon Electrode by Pseudo Phase Plane Method(Amer Scientific Publishers, 2011) Baleanu, Dumitru; Dinc, Erdal; Solak, Ali Osman; Eksi, Haslet; Guzel, Remziye; Tenreiro Machado, J. A.; MacHado, J.A. TenreiroThis paper presents the Pseudo phase plane (PPP) method for detecting the existence of a nanofilm on the nitroazobenzene-modified glassy carbon electrode (NAB-GC) system. This modified electrode systems and nitroazobenze-nanofilnn were prepared by the electrochemical reduction of diazonium salt of NAB at the glassy carbon electrodes (GCE) in nonaqueous media. The IR spectra of the bare glassy carbon electrodes (GCE), the NAB-GC electrode system and the organic NAB film were recorded. The IR data of the bare GC, NAB-GC and NAB film were categorized into five series consisting of FILM1, GC-NAB1, GC1; FILM2, GC-NAB2, GC2; FILM3, GC-NAB3, GC3 and FILM4, GC-NAB4, GC4 respectively. The PPP approach was applied to each group of the data of unmodified and modified electrode systems with nanofilm. The results provided by PPP method show the existence of the NAB film on the modified GC electrode.Article Citation - WoS: 203Citation - Scopus: 210On Exact Traveling-Wave Solutions for Local Fractional Korteweg-De Vries Equation(Aip Publishing, 2016) Tenreiro Machado, J. A.; Baleanu, Dumitru; Cattani, Carlo; Yang, Xiao-JunThis paper investigates the Korteweg-de Vries equation within the scope of the local fractional derivative formulation. The exact traveling wave solutions of non-differentiable type with the generalized functions defined on Cantor sets are analyzed. The results for the non-differentiable solutions when fractal dimension is 1 are also discussed. It is shown that the exact solutions for the local fractional Korteweg-de Vries equation characterize the fractal wave on shallow water surfaces. Published by AIP Publishing.Article Citation - WoS: 4Citation - Scopus: 6Analysis of Uv Spectral Bands Using Multidimensional Scaling(Springer London Ltd, 2015) Dinc, Erdal; Baleanu, Dumitru; Tenreiro Machado, J. A.; Machado, J. A. TenreiroThis study describes the change of the ultraviolet spectral bands starting from 0.1 to 5.0 nm slit width in the spectral range of 200-400 nm. The analysis of the spectral bands is carried out by using the multidimensional scaling (MDS) approach to reach the latent spectral background. This approach indicates that 0.1 nm slit width gives higher-order noise together with better spectral details. Thus, 5.0 nm slit width possesses the higher peak amplitude and lower-order noise together with poor spectral details. In the above-mentioned conditions, the main problem is to find the relationship between the spectral band properties and the slit width. For this aim, the MDS tool is to used recognize the hidden information of the ultraviolet spectra of sildenafil citrate by using a Shimadzu UV-VIS 2550, which is in the world the best double monochromator instrument. In this study, the proposed mathematical approach gives the rich findings for the efficient use of the spectrophotometer in the qualitative and quantitative studies.Article Citation - WoS: 9Citation - Scopus: 14Characterization Approach To Modified Glassy Carbon Electrode-Nanofilm System Within Multidimensional Scaling(Amer Scientific Publishers, 2011) Baleanu, Dumitru; Dinc, Erdal; Solak, All Osman; Eksi, Haslet; Guzel, Remziye; Tenreiro Machado, J. A.; Machado, J. A. TenreiroThe aim of this work is to characterize the nanofilm consisting of the benzoic acid-modified glassy carbon (GC) electrode system through multidimensional scaling space analysis. The surface modification is based on the electrochemical reaction between the GC electrode and benzoic acid-diazonium salt (BA-DAS). As a result, the nonofilms regarding the benzoic acid-glassy carbon (BA-GC) electrode surface was obtained. For the analysis of the naonfilm of BC-GC electrode system, the IR spectra of the modified BA-GC electrode surface, GC surface and BA-DAS were recorded in the spectral range of 599.84 - 3996.34 [cm(-1)]. The IR data vectors of the above three forms were processed by the using the multidimensional scaling space approach to demonstrate the existence of a nanofilm on the modified BA-GC electrode system. Two- and three-dimensional MDS profiles obtained by application of multidimensional scaling approach to the data sets {CG1, ... ,CG10}, {BA-GC1, ... ,BA-GC10} and {FILM1, ... ,FILM10} allow a good recognition of the nanofilm on the modified glassy carbon (GC) electrode system.